estimation of individual probabilities of covid-19 ...jun 06, 2020 · symbol parameter description...

Estimation of Individual Probabilities of COVID-19 Infection, Hospitalization, and 1

Death From A County-level Contact of Unknown infection Status 2

3

Rajiv Bhatia MD, MPH * 4

Assistant Professor of Medicine (affiliated), Stanford University 5

Physician, VA Palo Alto Health Care System 6

[email protected] 7

Jeffrey Klausner, MD, MPH 8

Professor of Medicine and Public Health, UCLA 9

[email protected] 10

11

Abstract: - 230 words 12

Manuscript: 2747 words 13

References: 822 words 14

Tables: 3 15

Figures: 2 16

17

* Corresponding Author 18

19

Version Date: June 23, 2020 20

. CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 24, 2020. ; https://doi.org/10.1101/2020.06.06.20124446doi: medRxiv preprint

NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.

https://doi.org/10.1101/2020.06.06.20124446

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Abstract 21

Objective: Our objective is to demonstrate a method to estimate the probability of a 22

laboratory confirmed COVID19 infection, hospitalization, and death arising from a 23

contact with an individual of unknown infection status. 24

Methods: We calculate the probability of a confirmed infection, hospitalization, and 25

death resulting from a county-level person-contact using available data on current case 26

incidence, secondary attack rates, infectious periods, asymptomatic infections, and 27

ratios of confirmed infections to hospitalizations and fatalities. 28

Results: Among US counties with populations greater than 500,000 people, during the 29

week ending June 13,2020, the median estimate of the county level probability of a 30

confirmed infection is 1 infection in 40,500 person contacts (Range: 10,100 to 586,000). 31

For a 50 to 64 year-old individual, the median estimate of the county level probability of 32

a hospitalization is 1 in 709,000 person contacts (Range: 177,000 to 10,200,000) and 33

the median estimate of the county level probability of a fatality is 1 in 6,670,000 person 34

contacts (Range 1,680,000 to 97,600.000). 35

Conclusions and Relevance: Estimates of the individual probabilities of COVID19 36

infection, hospitalization and death vary widely but may not align with public risk 37

perceptions. Systematically collected and publicly reported data on infection incidence 38

by, for example, the setting of exposure, type of residence and occupation would allow 39

more precise estimates of probabilities than possible with currently available public 40

data. Calculation of secondary attack rates by setting and better measures of the 41

prevalence of seropositivity would further improve those estimates. 42



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Introduction 43

44

During infectious disease epidemics, human perception of risk modifies disease 45

transmission, and motivates, or not, protective behaviors such as hand hygiene, 46

wearing masks and social distancing at the individual level and quarantine, travel 47

restrictions, and restrictions on gatherings at the societal level. Novel infectious agents 48

such as the COVID-19 virus, with immature understanding of susceptibility, 49

transmission, and lethality, challenge accurate risk estimation. 50

51

Predictive models, government surveillance, and epidemiological studies have 52

characterized the risk of COVID-19, in terms of aggregate, and not individual, 53

outcomes, primarily including County-level counts of reported infections, 54

hospitalizations, and deaths. (1) Research has attempted to estimate case fatality rates 55

and identified risk factors for adverse outcomes from COVID-19 disease, such age and 56

chronic disease status. (2, 3) We are not aware of any published research that 57

estimates individual level probabilities of infection, hospitalization, and death from 58

exposure in the general community. 59

60

In the United States, publicly accessible data does not yet permit estimating the 61

individual risks of COVID-19 transmission in specific exposure settings, including 62

workplaces, prisons, nursing homes, hospitals and group residential housing settings. 63

However, a starting point for estimation can be the average individual-level probability of 64

acquiring infection across all settings at the level of a county. One can modify those 65



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estimates as data on setting specific infection incidence rates, susceptibility and 66

secondary attack rates permit. 67

68

Here, we contribute to COVID-19 risk assessment by demonstrating a method to 69

estimate the individual probabilities of acquiring infection, being hospitalized, and dying 70

in U.S. Counties. We identify areas of available and future knowledge that could make 71

risk assessment more precise and context specific. 72

73

Materials and Methods 74

75

Our objective is to estimate the probability of acquiring COVID-19 infection from a 76

“contact” with a random individual of unknown infection status. We conceptualize this 77

probability under steady state conditions (e.g. no epidemic growth or decline) as a 78

function of individual susceptibility, the current reported case incidence, accounting for 79

undetected infection, the share of infection transmission occurring without a known 80

contact, the chance of transmission per contact (e.g., the secondary attack rate), and 81

the duration of infectiousness, accounting for pre-symptomatic transmission. 82

83

We use the formulae below to compute probabilities of infection, confirmed infection, 84

hospitalization, and death. 85

86

(1) P infection | contact = S I confirmed C β [1+ α/(1 – α) ] [ σ D Infectious + η (1- σ) D Infectious ] 87

(2) P confirmed-infection | contact = P infection| contact / (1- α) 88

(3) P hospitalization | contact = CHR × P confirmed-infection | contact 89



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(4) P death | contact = CFR × P confirmed-infection| contact 90

91

We describe the parameters used in Table 1 and explain their sources below. 92

Table 1. Parameters Used in Formulae 93

94

a US CDC COVID-19 Pandemic Planning Scenarios. Scenario 4 Estimates 95

96

Symbol Parameter Description Value

S Proportion of the population susceptible 95%

Iconfirmed Incidence of confirmed (reported) infections per day County Data

C Proportion of infections resulting from unknown contacts 100%

α Proportion of total infections unconfirmed (undetected

and unreported) 75%

Β Probability of infection per exposure 10%

Dinfectious Average days infectious per infection 8

σ Proportion of infectious period pre-symptomatic a 40%

η Proportion non-compliant with isolation 25%

CHR Case Hospitalization Ratio, 0 to 49 years a 0.026

CHR Case Hospitalization Ratio, 50 to 64 years a 0.057

CHR Case Hospitalization Ratio, Over 65 years a 0.1

CFR Case Fatality Ratio, 0 to 49 years a 0.001

CFR Case Fatality Ratio, 50 to 64 years a 0.006

CFR Case Fatality Ratio, Over 65 years a 0.032



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97

The prevalence of susceptibility to COVID-19 is unknown. Pre-existing immunity due to 98

previous COVID-19-related coronaviral infections is plausible but speculative. Reliable 99

estimates for the proportion of the population who have acquired immunity is unknown 100

but non-zero. We have conservatively estimated the prevalence of susceptibility to be 101

95%. 102

103

We acquired COVID-19 confirmed infection incidence data from publicly reported 104

statistics compiled by The New York Times. (4) Confirmed infection rates underestimate 105

the true incidence of infection in the community because of undetected infections that 106

can be both symptomatic and asymptomatic. Several studies have estimated the 107

asymptomatic fraction. (5-7) In one meta-analytic review, the proportion of 108

asymptomatic infections ranged from 6% to 41%. (8) A weighted mean estimate from 109

those studies suggests that about 1 out of 6 persons, or 16%, may be asymptomatic. 110

On the other hand, seroprevalence studies aim to capture both the confirmed and 111

unconfirmed fractions together without regard to symptoms. Some seroprevalence 112

studies suggest that up to 90% of infections may be unconfirmed. (9) The US CDC 113

gives 50% as their most conservative estimate of the proportion of asymptomatic 114

infections. (10) We estimate 75% of all infections are unconfirmed which includes both 115

symptomatic and asymptomatic unconfirmed infections. 116

117

Limited data is available on the share of reported infections arising without a known 118

contact. As of this date, the US CDC has not included any statistics on this attribute of 119



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confirmed infections. The State of Oregon currently publicly reports infections without a 120

known contact a varying between 30 and 50%%. Because of limited national data, we 121

use 100% for this parameter; we leave the parameter in the equation for the purpose of 122

future applications. 123

124

The attack rate for an exposure varies by exposure intensity, context, proximity, and 125

duration. For this analysis, contact means any substantive exposures that happen in a 126

community, household, workplaces, or group living situations. Examples of substantive 127

contacts outside households might include dining with a friend or business contact, 128

working in a shared office space or having close or physical contact without the types of 129

precautions now recommended for prevention of infection transmission (e.g. avoiding 130

handshaking, embraces, wearing a mask or indoor ventilation). We do not consider 131

contacts to be short-term events, such as passing by a person on the street. Contact 132

within households involves habitual and typically unprotected close physical. We 133

understand that attack rates will vary across such diverse exposure settings. 134

135

Overall, secondary attack rates from contact tracing studies on COVID-19 range from 136

0.7% to 16.3%. One study in Taiwan estimated a mean attack rate of 0.7% with an 137

attack rate of ~5% among household and non-household family contacts. (11) A Hong 138

Kong study of the quarantined contacts of visitors from China estimated a secondary 139

attack rate of 11.7%. (12) Two published study within China found a household attack 140

rate of 16.3% and 11.2% respectively. (13-14) 141

142



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We assume an average plausible attack rate across all settings of exposure based on 143

these range of estimates to be 10% in the absence of more setting and activity specific 144

data. We acknowledge that this estimate may overestimate the attack rate for a non-145

household contact and underestimate it for a household contact. 146

147

We estimate the total duration of infectiousness as 8 days. Research suggests that 148

individuals who develop symptoms may be infectious two to three days before the onset 149

of symptoms. (15) We apply the US CDC’s estimates that the proportion of 150

infectiousness before symptom onset is 40% of the total duration. (10) Conservatively, 151

we treat infections in the unreported fraction as being infectious for the same duration 152

as those with reported infections. 153

154

Compliance with self-isolation affects the number of infectious people circulating with 155

infection after symptoms develop. Current research within the context of the COVID-19 156

pandemic finds that compliance with isolation ranges from 57% without financial 157

compensation to 94% with compensation. (16) Given the current US context and the 158

availability of sick leave compensation, we assume that 75% of individuals with 159

confirmed infection will voluntarily self-isolate after symptoms develop. We do not alter 160

the duration of infectiousness for the unconfirmed fraction of infections. 161

162

We estimate the probabilities per contact of reported infections, hospitalizations and 163

deaths as fixed ratios of the estimated but unobserved probability of infection. The 164



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relationship between total infections and confirmed infections is fixed and defined by the 165

parameter alpha above. 166

167

We estimate the probability of hospitalizations and deaths per contact using US CDC 168

estimates of case hospitalization ratios and case fatality ratios from their pandemic 169

planning scenario four, which is their most conservative current estimate of disease 170

severity and transmissibility. (10) (Table 1) Based on these fixed ratios, we expect 18 171

reported infections and 70 total infections for every hospitalization in an individual in the 172

50-64 year old age group. And we expect 167 reported infections, and 667 total 173

infections for every death in the 50-64 year old age group. 174

175

These estimated case fatality ratios are within the range of published values in the 176

United States. One study of deaths through the early part of the epidemic estimated the 177

case fatality ratio for symptomatic cases to be 1.3% (95% CI: 0.6% to 2.1%). (2) 178

179

We compared estimated weekly hospitalization incidence rates produced using the 180

estimated probabilities per contact against observed incidence rates of laboratory 181

confirmed COVID-19 hospitalization in several US multi-county regions where the US 182

CDC conducts active hospital case surveillance. (17) To estimate weekly 183

hospitalizations, we multiplied our estimates of age specific probabilities of 184

hospitalization per contact and a modest number of daily contacts equal to the number 185

of other household members plus one. 186

187



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Results 188

189

Among US Counties with populations greater than 500,000 people (N= 1224), for the 190

week ending June 13, 2020, the median observed county-level daily case incidence is 191

6.78 per 100,000 (Range, 0.41- 24). In those counties, the median estimate of the 192

county-level probability of a confirmed COVID-19 infection is 1 infection in 40,500 193

person-contacts (Range: 10,100 - 586,000). These estimates reflect the probability per 194

contact at a single point in time averaged across all types of contacts and settings, 195

within and outside households. 196

197

In the same counties, for a 50 to 64 year old individual, , the median estimate of the 198

county-level probability of a hospitalization is 1 in 709,000 person-contacts (Range: 199

177,000 – 10,200,000) and the median estimate of the county-level probability of a 200

fatality is 1 in 6,670,000 person-contacts (Range 1,680,000 – 97,600.000). Table 2 lists 201

probabilities for other age groups. 202



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Table 2. Estimated County-level Probabilities for the Week Ending June 13, 2020 of 203

COVID-19 Events in Counties with Populations Greater Than 500,000 (N = 1224) 204

Event Age Group Average Median Minimum Maximum

Confirmed

Case

All 0.002833% 0.002470% 0.000171% 0.009892%

Hospitalization

Under 49 yr 0.000074% 0.000064% 0.000004% 0.000257%

50- 64 yr 0.000162% 0.000141% 0.000010% 0.000564%

Over 65 yr 0.000283% 0.000247% 0.000017% 0.000989%

Fatality

Under 49 yr 0.000003% 0.000002% 0.000000% 0.000010%

50- 64 yr 0.000017% 0.000015% 0.000001% 0.000059%

Over 65 yr 0.000091% 0.000079% 0.000005% 0.000317%

205

Figure 1 illustrates the average estimated probabilities of confirmed infection, 206

hospitalization and fatality per contact as a function of daily case incidence. Figure 2 207

Illustrates the estimated number of hospitalizations and fatalities per 1 million contacts 208

in a subset of analyzed US counties with populations greater than 1.5 million. 209

210

We found good concordance between the estimated weekly hospitalization rates and 211

rates from US CDC hospitalization surveillance data in most of our comparison regions 212

under the assumption that average daily contacts equaled the average number of other 213

household members plus one. (Table 3) CDC acknowledges that more recent data 214

values are subject to revision. 215



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Table 3. Estimated weekly hospitalization rates per 100,000 people for the week ending 216

June 13, 2020 compared to weekly laboratory confirmed hospitalization rates observed 217

by US CDC regional surveillance. 218

County A

lam

eda,

CA

Den

ver C

O

Fulto

n G

A

Mon

tgom

ery,

MD

Way

ne, M

I

Assumption of Contacts Per Day

2.8 2.3 2.47 2.79 2.52

Estimated Weekly New Cases per 100,000

32.94 37.55 28.2 127.4 53.8

Estimated Weekly Hospitalization Rate (per 100,0000 people)

18-49 years 0.86 0.98 0.7 3.3 1.4

50-64 years 1.88 2.14 1.6 7.3 3.1

Over 65 years 3.29 3.76 2.8 12.7 5.4

COVID-NET Observed Regional Weekly Hospitalization Rates

18-49 years 1 1.1 1 5.3 0.4

50-64 years 1 3.2 2 6.6 0.8

Over 65 years 3.3 2.2 1.7 13.5 0.5 219

220

Discussion 221

222

We demonstrate a method to estimate the average county-level probabilities of COVID-223

19 confirmed infections, hospitalizations, and deaths in the U.S resulting from a contact 224

with a random person in the population. Those estimates reflect current reported 225

COVID-19 confirmed infection incidence in US counties with more than 500,000 people 226

for the week ending June 6, 2020. Probabilities vary across a wide range reflecting the 227

varying case incidences in different counties. 228



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229

Our method is limited by the availability of publicly available data on infection 230

transmission on COVID-19, including setting and occupational specific case incidence 231

rates, data on antibody seroprevalence, the share of infection with known contacts, and 232

activity-specific attack rates. The estimates therefore reflect the average probability 233

across a wide range of exposure contexts. Nevertheless, observed rates of 234

hospitalization for laboratory confirmed COVID-19 disease in several US CDC active 235

surveillance areas generally corroborate our estimates under the assumption of a 236

modest level of social contact. 237

238

Our estimates of the average probabilities per contact do not accurately estimate risks 239

for specific subsets of people. Infections occur within geographically and socially 240

constrained chains of transmission, for example, within clusters of related or socially 241

connected individuals or among those living in congregate living facilities such as 242

nursing homes. Clusters of COVID-19 infections have been reported associated with 243

prisons, workers dormitories, religious services, nightclubs, schools, cruise ships, 244

sporting events, and professional conferences. (18) Disaggregating confirmed infection 245

incidence rates into fractions representing those with and without known contacts and 246

those within and without congregate living settings would allow for more setting and 247

population specific risk estimates. This requires the systematic public reporting of 248

confirmed infection exposure factors. 249

250



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As mentioned above, systematic data on the share of confirmed infections arising 251

without a known contact is not currently available. Appling this fraction to the model 252

would reduce our estimates based on the assumption of a 100% share. 253

254

Available estimates of the secondary attack rate come from observations outside the 255

US and at an earlier time period in the pandemic, prior to normalization of behaviors 256

that reduce the risk of infection transmission, such as increased hand washing, 257

observing physical distance, forgoing physical greetings, and wearing masks. 258

259

The limitations of published secondary attack rates and the lack of disaggregated data 260

on confirmed infection incidence also do not allow our estimates to differentiate between 261

community and household transmission. Most studies indicate that household attack 262

rates are higher than for contacts in the community. Systematic public reporting of 263

anonymized contact tracing data would provide information to assess context specific 264

attack rates. 265

266

We also cannot account for intra-individual variation in the secondary attack rate within 267

a setting. With respiratory viruses, the number of secondary cases generated by each 268

index case can vary significantly. (19-20) One recent estimate suggests that 80% of 269

COVID-19 infections are due to a small fraction (10%) of particularly infectious 270

individuals. (21) 271

272



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We have assumed a high fraction of the population remains susceptible as the 273

prevalence and significance of antibodies to COVID-19 is not known. However, there 274

may well be factors conferring protection to infection or responsible for differences in 275

susceptibility. For example, cross immunity due to infection with other coronaviruses 276

may be occurring. (22) Researchers have also observed cellular immune system 277

responses to COVID-19 among unexposed individuals likely due to prior exposure to 278

related coronaviruses. (23) More data will be required before adjusting risk assessment 279

for population susceptibility or immunity. 280

281

We estimated probabilities of hospitalization and death based on CDC estimates of 282

disease severity. We chose conservative scenarios but acknowledge that estimates of 283

confirmed infection fatality ratios may further evolve over the course of the pandemic. 284

Furthermore, individual states may have different criteria for recording a death from 285

COVID-19. The risk of hospitalization and death varies with other risk factors including 286

race/ethnicity, level of deprivation, and chronic diseases such as lung disease and 287

diabetes, that are not reflected in our analysis. 288

289

Better data to address the above limitations would likely reduce estimated probabilities 290

of adverse events for a large fraction of the population; still, the estimated probabilities 291

reported here may appear considerably lower than those reflected in public opinion 292

surveys. Scientific uncertainties, media attention, dramatic governmental action and a 293

subjective perceived lack of control over exposure all may be influencing risk 294

perception. Exploring methods to communicate risk and the concordance of perceived 295

risk and risk probabilities would be an appropriate subject for further work. 296



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297

Avoiding human contact in the setting of an uncertain and lethal epidemic threat is an 298

expected and self-protective human behavior. Prevalent beliefs today about the sources 299

of COVID-19 infection include ‘contact with infected persons’, ‘people coming from 300

abroad’ or ‘foreign nationals.’ (24) Notably, many people assume that contact with a 301

family member has a lower risk of infection transmission than contact with a stranger. 302

This may not be true for all subgroups in the population. 303

304

In the US, policy makers have taken dramatic and unprecedented steps to control 305

COVID-19, applying universal contact reductions through home confinement, limits on 306

travel, closures of schools and businesses and limits on gatherings. While heightened 307

perception of risk (e.g., fear) motivated these restrictions at the outset of the epidemic, 308

ongoing restrictions on community activity may be mediating risk perceptions. (25) 309

310

Notably, in Wuhan, the government limited exponential growth of the COVID-19 311

epidemic using isolation and quarantine, mandatory mask wearing, canceled New 312

Year’s celebrations, the curtailment of intra-city and intercity transportation and 313

extension of the New Year’s holiday period. (26) South Korea achieved epidemic control 314

with scaled up testing, strong contact notification practices, case isolation and strict 315

quarantine of those exposed and public awareness. (27) The lack of understanding of 316

how various countries have brought their epidemics under control maybe another 317

important factor influencing the perception of risk to COVID-19 infection in community 318

settings in the US. 319

320



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Return to community workplace and social life will require individuals to be comfortable 321

with their personal risk of acquiring COVID-19 infection. Estimates on the individual 322

probabilities of infection, hospitalization and death may contribute to a more accurate 323

risk perception. Systematically collected and publicly reported data on infection 324

incidence by, for example, the geographic setting of exposure, residence type, whether 325

a case had a known exposure, and would allow more precise estimation than those 326

possible with currently available public data. Calculation of secondary attack rates by 327

setting and prevalence of seropositivity would further improve these estimates. 328

329

Contributions: Rajiv Bhatia and Jeffrey Klausner equally contributed to the design of 330

the study and writing of the manuscript. Rajiv Bhatia conducted the analysis. 331

332

Conflicts of interest: None 333

Funding: None 334



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Figure 1. Estimated county-level probabilities of confirmed infection, hospitalization and

death per contact as a function of daily case incidence.



https://doi.org/10.1101/2020.06.06.20124446


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Figure 2. Estimated current number of predicted COVID-19 hospitalizations per 1 million

contacts in counties with populations greater than 1.5 million.



https://doi.org/10.1101/2020.06.06.20124446


estimation of individual probabilities of covid-19 ...jun 06, 2020 · symbol parameter description...

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